Statistical Inference in the Presence of Nuisance Parameters
The present final chapter studies a geometrical theory of statistical inference in the presence of nuisance parameters. When we fix the value of the parameter of interest while the nuisance parameters take any values, we have a submanifold in the model M depending on the fixed value. Statistical inference is carried out concerning the family of these submanifolds, so that their geometrical properties play an important role on evaluating inferential procedures. We first search for the possibility of reparametrizing the nuisance parameter such that it is always orthogonal to the parameter of interest. We next study the amount of information loss caused by not knowing the true value of the nuisance parameter. It is related to the mixture curvature of the submanifold defined by the nuisance parameter.
KeywordsTangent Space Statistical Inference Fisher Information Efficient Estimator Nuisance Parameter
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